ON THE LARGEST EIGENVALUE OF UNICYCLIC GRAPHS

Slobodan K. Simi\'c

Elektrotehnicki fakultet, Beograd, Yugoslavia

Abstract: We first establish some relations between the graph structure and its largest eigenvalue. Applying these results to unicyclic graphs (with a fixed number of points), we explain some facts about the $\lambda_1$-ordering of these graphs. Most of these facts were suggested by the experiments conducted on the expert system GRAPH, which has been developed and implemented at the Faculty of Electrical Engineering, University of Belgrade.